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## Abstract specification theory: an overview (2003)

Venue: | Logics of Engineering Software |

Citations: | 6 - 4 self |

### Citations

686 |
Categories for the working mathematician
- MacLane
- 1971
(Show Context)
Citation Context ... review the concepts needed, largely to fix our notation and terminology, referring to many of the standard textbooks and monographs onscategory theory for a fully formal presentation (with classical =-=[24]-=- still a primary reference; we add [35], with a presentation targeted at exactly the area we address here). Let us start with the most basic concepts. A category K consists of: • a class of objects: |... |

628 |
Model Theory
- Chang, Keisler
- 1989
(Show Context)
Citation Context ...❅ ❅ ❅ ❅ Σ θ � ��✒ σ2 � � ����✒ Figure 8: Interpolation property Interpolation is a very subtle and deep property. It is well-known that the standard (singlesorted) first-order logic has interpolation =-=[13]-=-; this carries over to the many-sorted case, butsonly for signature morphisms that are injective on sort names [10]. On the other hand, the equational logic EQ does not have interpolation as presented... |

576 |
Institutions: abstract model theory for specification and programming.
- Goguen, Burstall
- 1992
(Show Context)
Citation Context ...ication has not and could not lead to any specific “best” system, suitable for every need that may arise in the theory and practice of software specification. Therefore, following Goguen and Burstall =-=[19]-=-, rather than engaging in a futile search for a unique ideal system, we propose to abstract away from the details of whatever logical system one may want to use, and develop at least the basic concept... |

302 |
An initial algebra approach to the specification, correctness, and implementation of abstract data types”, Current Trends in Programming Methodology,
- Goguen, Thatcher, et al.
- 1978
(Show Context)
Citation Context ...ications with initial algebra semantics. What remained of the purely algebraic tradition of equational algebra, as perhaps first introduced to software specification in its pure form by the ADJ group =-=[21]-=-, is primarily the stress on the semantic view of software, with programs modeled essentially as algebras. Indeed: software ∗ This work has been partially supported by KBN grant 7T11C 002 21 and Europ... |

256 | Combinatorial approaches to finding subtle signals in dna sequences
- Pevzner, Sze
(Show Context)
Citation Context ...at the above explanations are sufficient to look through the following example, motivated by the problem of searching for a “motif” in DNA sequences (hence somewhat pretentious terminology here), see =-=[30]-=- 3 . In essence, we specify a function that given a set of sequences, finds a pattern of each length that is most similar to some subsequence of each of the sequences in the set. (We refer to Sect. 2.... |

181 |
The Semantics of Clear, A Specification Language
- Burstall, Goguen
- 1980
(Show Context)
Citation Context ... This indicates that one way to alleviate the shortcomings of equational specifications is to additionally equip them with extra-logical constraints (the terminology originates from the work on CLEAR =-=[12]-=-): • reachability constraint: imposes “no junk” condition, which requires that all carrier elements in algebras considered are values of closed terms. This is further generalized to generation constra... |

166 |
Fundamentals of Algebraic Specification 1: Equations and Initial Semantics.
- Ehrig, Mahr
- 1985
(Show Context)
Citation Context ...ect to verification and analysis are the expected and practically important norm, and apply to a wide variety of approaches. The ideas we present here grew on the tradition of algebraic specification =-=[16, 43]-=-, although there is by now much more flexibility and power here than in traditional algebraic specifications, dominated by equational specifications with initial algebra semantics. What remained of th... |

143 | Software Requirements: Analysis and Specification. - Davis - 1990 |

129 |
Principles of parameterized programming
- Goguen
- 1989
(Show Context)
Citation Context ...hink of such parts as pieces of code. To accommodate them in our view of refinement steps, we introduce another component here, a constructor, which intuitively corresponds to a parameterized program =-=[18]-=-, or a parameterized module, like a STANDARD ML functor [29]. Semantically such constructors are just functions that map models to models; we will classify them by the signatures of their arguments an... |

114 |
Heterogeneous algebras,
- Birkhoff, Lipson
- 1970
(Show Context)
Citation Context ...to be made precise. In fact, these concepts have been a topic of study of universal algebra for years [23], and we can draw on all this work, adapting it slightly to the many-sorted (or heterogeneous =-=[9]-=-) framework naturally emerging in computer-science applications. We briefly review these concepts here, mainly to fix the notation — referring for instance to [34] for a more complete account. An alge... |

92 | Specifications in an arbitrary institution
- Sannella, Tarlecki
- 1988
(Show Context)
Citation Context ...mechanisms used to build complex specifications by manipulating and putting together simpler and presumably well-understood ones. This again originates with CLEAR, and has been further put forward in =-=[32]-=- by insisting that specification-building operations should be defined in a manner as independent of the underlying institution as possible. We will continue working here within a fixed, but otherwise... |

71 | Completeness of many-sorted equational logic
- Goguen, Meseguer
- 1985
(Show Context)
Citation Context ...e here is that in the many-sorted framework (unlike in the traditional, single-sorted algebra) one is forced to pay a special attention to the set of variables over which the equations are considered =-=[20]-=-. For instance, over a signature with constants a and b and a unary operation f, a = b is not a consequence of a = f(x) and f(x) = b (unless there is a closed term of the argument sort of f).sSemantic... |

70 |
eds., Introduction to HOL: A Theorem Proving Environment for Higher Order Logic,
- Gordon, Melham
- 1993
(Show Context)
Citation Context ...tutions: • EQ — equational logic; • FOEQ — first-order logic (with predicates and equality); • PEQ, PFOEQ — as above, but with partial operations; • HOL — higher-order logic (say, in the HOL version, =-=[22]-=-); • logics of constraints (fitted via signature morphisms); • CASL — the logic of CASL: partial first-order logic with equality, predicates, generation constraints, and subsorting. Just to show how m... |

61 | CASL: the Common Algebraic Specification Language.
- Astesiano, Bidoit, et al.
- 2002
(Show Context)
Citation Context ...hematical rigor and precision (Sect. 2). We discuss then the very concept of a specification (Sect. 3.1) and sketch some of specification mechanisms present in many formalisms (Sect. 3.2) and in CASL =-=[1, 14]-=- in particular (Sect. 3.3). A formal view of the process of software development is presented in Sect. 3.4, leading to the issues of modular design, discussed in Sect. 4 using the concept of architect... |

61 | Essential concepts of algebraic specification and program development - Sannella, Tarlecki - 1997 |

51 |
Axioms for abstract model theory
- Barwise
- 1972
(Show Context)
Citation Context ...s has been provided in a form adequate for the purposes of abstract specification theory (and not only for this) via the notion of institution, formed very much in the spirit of abstract model theory =-=[2, 3]-=-. We refer to the original paper on institutions [19] and to [42, 36] for a more exhaustive presentation of this concept and the related theory, limiting the presentation here to the basic definition,... |

47 |
Data Abstraction and the Correctness of Modular Programming
- Schoett
- 1987
(Show Context)
Citation Context ...ation, we admit doing so up to observational equivalence only (allowing the construction to yield results in Abs[SP ′ ]). Perhaps surprisingly, this can be made to work under an additional assumption =-=[38]-=-. A constructor κ: Alg(Σ) → Alg(Σ ′ ) is stable if it preserves NOsobservational equivalence of algebras: for all A, B ∈ Alg(Σ), A ≡ B =⇒ κ(A) ≡ κ(B). If we now assume all the constructors involved to... |

46 | Logical systems for structured specifications.
- Borzyszkowski
- 2002
(Show Context)
Citation Context ...d proofs are reduced to the proof search for consequences of a typically huge (and totally unstructured here) set Φall. A much bettersproof system is given by the rules in Fig. 9. Following [32] (cf. =-=[11]-=- for full analysis), we give a proof rule for each of the specification-building operations, allowing the user to reduce deriving consequences of the overall specification to deriving consequences of ... |

33 |
Algebraic specification, in Handbook of Theoretical Computer
- Wirsing
- 1989
(Show Context)
Citation Context ...ect to verification and analysis are the expected and practically important norm, and apply to a wide variety of approaches. The ideas we present here grew on the tradition of algebraic specification =-=[16, 43]-=-, although there is by now much more flexibility and power here than in traditional algebraic specifications, dominated by equational specifications with initial algebra semantics. What remained of th... |

31 | Structured theories in LCF
- Sannella, Burstall
- 1983
(Show Context)
Citation Context ...onents of the overall specification, thus allowing the irrelevant parts to be disregarded. This can be exploited in a proof support system for structured specifications, as perhaps first indicated in =-=[31]-=-. ϕ ∈ Φ 〈Σ, Φ〉 ⊢ ϕ SP 1 ⊢ ϕ SP 1 ∪ SP 2 ⊢ ϕ SP ⊢ ϕ σ(SP) ⊢ σ(ϕ) SP ′ ⊢ σ(ϕ) SP ′ σ ⊢ ϕ SP 2 ⊢ ϕ SP 1 ∪ SP 2 ⊢ ϕ SP ⊢ ϕ1 · · · SP ⊢ ϕn {ϕ1, . . . , ϕn} ⊢ ϕ SP ⊢ ϕ Figure 9: Compositional proof system f... |

28 | Behavioural satisfaction and equivalence in concrete model categories
- Bidoit, Tarlecki
- 1059
(Show Context)
Citation Context ...g an arbitrary signature morphism). Where the intuition is clear, it coincides with the observational interpretation based on external algebra equivalence (see [4] for a more complete discussion, and =-=[8]-=- for an institution-independent formulation): Fact 13. For any equational basic specification 〈Σ, Φ〉, AbsOBS[〈Σ, Φ〉] = Mod ≈OBS [〈Σ, Φ〉]. 5.2 Observational Refinements The observational interpretation... |

27 |
Modularizing the formal description of a database system
- Fitzgerald, Jones
- 1990
(Show Context)
Citation Context ...uirements specifications and criteria for their quality are quite different from those for structuring final programs and the quality of the modular structure designed in the development process (see =-=[17]-=- for an early explicit discussion of this point). Consequently, instead of aiming at useful, but restrictive development rules of the form: NO SP ′ 1 κ1 ∼∼∼> SP 1 · · · SP ′ n κn ∼∼∼> SP n sbo(SP ′ 1,... |

26 | Institution: An Abstract Framework for Formal Specifications, In
- Tarlecki
- 1999
(Show Context)
Citation Context ... specification theory (and not only for this) via the notion of institution, formed very much in the spirit of abstract model theory [2, 3]. We refer to the original paper on institutions [19] and to =-=[42, 36]-=- for a more exhaustive presentation of this concept and the related theory, limiting the presentation here to the basic definition, a list of a few examples, and an abstract formulation of some logica... |

23 |
Foundations of Algebraic Specifications and Formal Program Development
- Sannella, Tarlecki
(Show Context)
Citation Context ... fix our notation and terminology, referring to many of the standard textbooks and monographs onscategory theory for a fully formal presentation (with classical [24] still a primary reference; we add =-=[35]-=-, with a presentation targeted at exactly the area we address here). Let us start with the most basic concepts. A category K consists of: • a class of objects: |K|; the category is small if this is a ... |

19 |
Universal Algebra, 2nd edition
- Grätzer
- 1979
(Show Context)
Citation Context ... the “software-engineering” concepts will be left unexplained in this paper, the right column has to be made precise. In fact, these concepts have been a topic of study of universal algebra for years =-=[23]-=-, and we can draw on all this work, adapting it slightly to the many-sorted (or heterogeneous [9]) framework naturally emerging in computer-science applications. We briefly review these concepts here,... |

17 |
Feferman (eds.), Model-theoretic logics
- Barwise, S
- 1985
(Show Context)
Citation Context ...s has been provided in a form adequate for the purposes of abstract specification theory (and not only for this) via the notion of institution, formed very much in the spirit of abstract model theory =-=[2, 3]-=-. We refer to the original paper on institutions [19] and to [42, 36] for a more exhaustive presentation of this concept and the related theory, limiting the presentation here to the basic definition,... |

16 | Extending development graphs with hiding
- Mossakowski, Autexier, et al.
- 2001
(Show Context)
Citation Context ...e to be used, which allow for the use of normal forms for structured specifications only if really necessary, maintaining the structure of specifications to guide the proof search as much as possible =-=[28]-=-. The proof system for consequences of structured specifications may be used also to establish that one specification is stronger than another; the corresponding compositional rules are given in Fig. ... |

12 |
Behavioural and abstractor specifications. Science of Computer Programming 25:149–186
- Bidoit, Hennicker, et al.
- 1995
(Show Context)
Citation Context ...of a translation of a specification along an arbitrary signature morphism). Where the intuition is clear, it coincides with the observational interpretation based on external algebra equivalence (see =-=[4]-=- for a more complete discussion, and [8] for an institution-independent formulation): Fact 13. For any equational basic specification 〈Σ, Φ〉, AbsOBS[〈Σ, Φ〉] = Mod ≈OBS [〈Σ, Φ〉]. 5.2 Observational Refi... |

12 |
Specification in an arbitrary institution with symbols
- Mossakowski
- 2000
(Show Context)
Citation Context ...4, with diagrams helping to read the more complicated rules for unit application and amalgamation in Fig. 15. The use of signaturesunion requires a bit more structure on the signature category (as in =-=[27]-=-, for instance), but the intended meaning should be clear. ΣG Σ ′ G Σ ′′ θ ✲ ι ✲ G ′′ ✻ ✻ i i ′ Model Semantics ΣT ✻ σ Σ ι ′ ι Σ ′ ✲ T ✻ σ ′ Σ ′ ✲ θ1 Σ1 G ❍ ✻ ❍❍❍❍❍❍❍❍❍❍❍❥ i1 θ ′ 2 ΣG Σ2 Σ1 Σ1 ∪ Σ2 Σ ... |

12 |
ML for the Working Programmer. Cambridge Univ
- Paulson
- 1991
(Show Context)
Citation Context ... our view of refinement steps, we introduce another component here, a constructor, which intuitively corresponds to a parameterized program [18], or a parameterized module, like a STANDARD ML functor =-=[29]-=-. Semantically such constructors are just functions that map models to models; we will classify them by the signatures of their arguments and of their results. This leads to the following definition: ... |

11 |
Generalized interpolation
- Borzyszkowski
- 2000
(Show Context)
Citation Context ...t is well-known that the standard (singlesorted) first-order logic has interpolation [13]; this carries over to the many-sorted case, butsonly for signature morphisms that are injective on sort names =-=[10]-=-. On the other hand, the equational logic EQ does not have interpolation as presented here; for signature morphisms injective on sort names, EQ has interpolation in a version that allows sets of inter... |

11 |
Completeness of proof systems for equational specifications
- MacQueen, Sannella
- 1985
(Show Context)
Citation Context ... may be used similarly. A warning: when initiality or reachability constraints are permitted, there can be no sound and complete finitary proof system for deriving consequences of such specifications =-=[25]-=-. Adding constraints to our specifications in fact means that we go beyond equational logic to increase the definitional power of our specification. This is just one example: other logical systems of ... |

10 |
Moving between logical systems. Recent Trends in Data Type Specifications. Selected Papers
- Tarlecki
- 1995
(Show Context)
Citation Context ... specifications spanning a variety of logical systems used conveniently to capture various aspects of the same program in various parts of a specification or at various phases of program development (=-=[40, 41]-=- offer but a starting point for such topics). What we have illustrated here is that the notion of an institution may well be used to separate the institution-dependent “kernel” of a specification form... |

9 | 2002b) Global development via local observational construction steps
- Bidoit, Sannella, et al.
(Show Context)
Citation Context ...chitectural specification of CASL [5]. To include some technical novelty, we outline a formal semantics and a proof calculus for a fragment of CASL architectural specifications, extending the work in =-=[6, 39]-=-. Observational interpretation of specifications and its consequences for the concepts underlying our view of software development, including the semantics and proof calculus for architectural specifi... |

6 |
General logic. Logic Colloquium'87
- Meseguer
- 1989
(Show Context)
Citation Context ...nt to be sound: Φ ⊢Σ ϕ =⇒ Φ |=Σ ϕ, and discuss its completeness: Φ |=Σ ϕ =⇒ Φ ⊢Σ ϕ, for Φ ⊆ Sen(Σ) and ϕ ∈ Sen(Σ). The resulting extension of the notion of institution has been named general logic in =-=[26]-=-. With the intuition inherited from Sect. 2.3, it should be clear that we may use colimits (in particular, pushouts) in Sign to combine signatures. Interestingly, colimits at the level of signatures c... |

5 | Toward component-oriented formal software development: an algebraic approach - Bidoit, Sannella, et al. - 2002 |

3 |
A.: Algebraic Preliminaries, in: Algebraic Foundations of Systems Specification
- Sannella, Tarlecki
- 1999
(Show Context)
Citation Context ... to the many-sorted (or heterogeneous [9]) framework naturally emerging in computer-science applications. We briefly review these concepts here, mainly to fix the notation — referring for instance to =-=[34]-=- for a more complete account. An algebraic (many-sorted) signature Σ = (S, Ω) consists of a set S of sort names and of a set Ω = 〈Ωw,s〉w∈S ∗ ,s∈S of operation names, classified by their arity and resu... |

3 |
Specification languages, Algebraic Foundations of Systems Specifications
- Sannella, Wirsing
- 1999
(Show Context)
Citation Context ...m become amenable to formal analysis. We will not dwell on the actual syntax of our specifications. There have been quite a number of specifications languages designed, starting with CLEAR [12] — see =-=[37]-=- for an overview. CASL [1, 14] is a recent development in this area; we have already used it in examples, and will continue doing so (with a bit more explanation in Sect. 3.3 below). What matters for ... |

1 |
Working with an arbitrary logical system
- Sannella, Tarlecki
(Show Context)
Citation Context ... specification theory (and not only for this) via the notion of institution, formed very much in the spirit of abstract model theory [2, 3]. We refer to the original paper on institutions [19] and to =-=[42, 36]-=- for a more exhaustive presentation of this concept and the related theory, limiting the presentation here to the basic definition, a list of a few examples, and an abstract formulation of some logica... |

1 |
Toward heterogeneous specifications. In: Frontiers of Combining Systems 2
- Tarlecki
- 2000
(Show Context)
Citation Context ... specifications spanning a variety of logical systems used conveniently to capture various aspects of the same program in various parts of a specification or at various phases of program development (=-=[40, 41]-=- offer but a starting point for such topics). What we have illustrated here is that the notion of an institution may well be used to separate the institution-dependent “kernel” of a specification form... |